Hello Christopher
First of all, I will say ‘you are on the right track’. LinkedIn is the best choice for your business. Here are some ways of lead generation.
1. Take a part in group discussions and be active.
2. Share regular updates on personal profile and company page.
3. Promote your product in ‘LinkedIn promotions’
4. Try running LinkedIn advertisement.
5. Integrate Twitter with Linkedin
These activities will give you results in a long run.
Thanks.